Three-loop beta-functions and anomalous dimensions in the Standard Model1

Abstract. In this talk the methods and computer tools which were used in our recent calculation of the three-loop Standard Model renormalization group coefficients are discussed. A brief review of the techniques based on special features of dimensional regularization and minimal subtraction schemes is given. Our treatment of γ5 is presented in some details. In addition, for a reasonable set of initial parameters the numerical estimates of the obtained three-loop contributions are presented. The renormalization group (RG) proves to be a useful and powerful tool in studying high-energy behavior of the Standard Model. Before the discovery of the Higgs boson RG equations (RGE) were used, among other things, to bound the value of the Higgs self-coupling. However, the bounds significantly depends on the scale at which one expects the appearance of New Physics. The observation of the Higgs boson in 2012 [1, 2] in some sense finalizes the SM since the information about the values of all the SM couplings become available from experiments. Due to this fact, the interest to RG studies of the Standard Model arises again, but at a new level of precision. One- and two-loop results for SM beta-functions have been known for quite a long time [3] and are summarized in [4]